Laegna Base Alphabet

 
Laegna uttmost basic alphabet with trivial letters
Laegna Essential (symbolizing the ideal world beyond the real world; starting from E read it from down to up, jumping from beginning to end, starting from E and thus ending at I, to form the forecoming next table):
A
B
C
D
ㅤ
ㅤ
E
F
G
H
ㅤ
ㅤ
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
⋂
ㅤ
ㅤ
Laegna Zero-oriented alphabet:
E
F
G
H
ㅤ
ㅤ
A
B
C
D
ㅤ
ㅤ
U
V
W
⋂
ㅤ
ㅤ
O
P
Q
R
S
T
I
J
K
L
M
N
Laegna Infinity-oriented alphabet (use one or two accents - ´ or ´´ - depending on whether you are having the accent-line in half octaves as in my example or two octaves - btw. “half” in Laegna division operator can mean what “two” means otherwise, meaning that I’m not reversing anything - ideal division and multiplication applies operations from higher octave to lower octave, utilizing the center, the top and bottom frequencies to find an effect, where it does not reverse at zero but the same effect amplifies; while this is linear operation, polar operations are still used - linear and polar in other meaning than in number system logecopositional orders):
I/Í
J/J́
K/Ḱ
L/Ĺ
M/Ḿ
N/Ń
O/Ó
P/Ṕ
Q/Q́
R/Ŕ
S/Ś
T/T́
U
V
W
⋂/
ㅤ
ㅤ
A
B
C
D
ㅤ
ㅤ
E
F
G
H
ㅤ
ㅤ
Btw. U and ⋂, which should look like upside-down u not well like an union operation I found from utf font, are reflected, but each reflection is possible in Laegna - this reflection is the only one where reflected word is directly in base alphabet and thus in normalized writings.
 
All the combinations and even transformations of letter are allowed, but consider:
  • Normalized text is utilizing the base alphabet described here, with accents, but in each word there should be not more than one or two accents, which rather move the line of the whole word (it’s frequency in octave shift) in relations to this; mostly adding more than two letters in a word means that it either sounds or is a number.
  • Poetic language, for expressivity reasons, can use more accents, reflections and transformations of letters. In intermediate calculations, more letters are also used as you cannot normalize before seeing rather complete answer, even if one letter, and thus while you intuitively select the projection or number representation, it’s allowed that you encounter words, which need letters now outside of your normal space, or similar transformations leading to strange projections. Once you reach to conclusions and results, in my typical script they are written in 1, 2 or 4 digits such as business plan would contain “E” as estimation of income, or if it needs to arrange them in more complex relations, “EEEE” would remind of ideal, where EEAE and EEEA would order near-perfections into some preferration. You express the mathologecal relations rather than real numbers, and you can add the long numbers in brackets in compressed format, rather in background utilizing something like less contrasted colors or fonts, or italic. With this kind of selection you make decisions and choises, and comparisons of estimations of their true value, but you need special time to go through the real science and engineering of numbers. Laegna numbers have “face value”, where different number formats and scripts give number systems with different formats, but the generic rules make the psychological appearance rather similar; for example positive numbers 1-4 in positive natural system would have the median line at the middle, excess at the top and lack in the bottom of frequencies of numbers, where you have created reliable number space - straight UUUU number, for example, would go 4 steps towards U value in infinity, where U would do one step in the same direction (step has character width, measured in angles of edges of mean circles with radius equal to value of your number). In -2 to 2 system, indeed the numbers are very different, but they are rather meant to express scales, where the neutral value is 0, and thus in psychological sense about what you do with this value they are still equal (you get those types of different numbers for real). Before the numbers are balanced in R and T, they can create random forms and not fit, so the psychological effect is weaker, but it does not go away - you can still trust some statistical appearance of basic numbers. Moreover, numbers of different lengths have similar face value if the digits are similar, but repeated more or less time.
 
Z, X, Y (also uttmost basic to Laegna):
These are frequential zones, where X is your current coordinate system and Z and Y are below and above; exact units of numbers like ZZZ for at least 3 octaves down normally would be given along with calculations, but the psychological behaviour is similar - both Z and ZZZ are more or less kind of positives far below zero (sub-zero) and in psychological approach, the multipliers can be rather related by obvious relations in size, rather than exactly calculated. This is especially true because many Laegna theorems do not depend on exact values, rather on number properties applied on probability scales - you can go deep in science but often, you just want fast impressions, summaries and general understandings, like is it good or evil thing.
 
Laegna basic extensions to alphabet
 
Note: the greek letters, very often are written in words, such as writing Taú instead of ´τ - this, because they are heavily accented letters and it might be insulting to express them with one digits, as if they were small numbers; they are also sometimes highlighted for the same purpose, such as writing ´τ (empathized, instantly noticeable) instead of ´τ or ´τ (miniaturized, less visible, less remarkable or perhaps the boring actual source of the fact you don’t want to read but your professor wants, reading small letters with glasses in your legal documents where titles are really worth it haha joke).
 
Symbols of harmonic growth and synergizing frequencies (starting from realm of God and angels, or a good demon)
h-harmony: a letter like m with longer line and 45 degree cross at the top of the line, and with two curved parts like m not one like n (it’s a christian cross - the extraspiritual symbol like this is rather using christian than buddhist symbolics like yinyang symbol of Laegna). This is the harmony, integrity, union or perhaps love.
step to h-harmony: is the same symbol, but not like m with extended first line and cross, but like n with the same features. This is growth with vision.
While harmonics create ten (four) with disharmonics, forming sequence you can write as mi, mo, ha and he for nü, mü, towards-h-harmonic and h-harmonic, you can extend this by internal opposites:
 
Opposites of harmonics have the first line of h or hn harmonics moved downwards so that the highest point fits the highest point of “n-part” of the visual letter, like p, and forms the cross below and not above. If you want to say for example that ideals have opposites, which are not necessarily evil.
 
Symbols of loss and evil will, rather opposites of harmonics (starting from realm of Satan and demons, or a bad demon)
nu (est. nüü): this one looks rather like mu in greek, like componentized to |ü. This means that you have wasted so much resources of others that in karmic cycle, you already wasted your resources also as you don’t know more people affected by your past good karma.
mu (est. müü): a letter like μ̈ in greek, with this shape and two dots on the part which looks like u, but it’s the Laegna not greek letter and thus this one has two u-parts, looking rather like |üü componentwise. This is rather unreasonable wasting of resources of others.
 
Optionally, in Laegna, you can have the first line poining below - μ̈ or above, where it looks more like h with u direction instead of n direction, but the first line in this higher position. While this might be the difference of fonts (I have a few optional elements for style), it could be a four-value or destructive ten, rather direason or dìharmonics, to say “ten” in negative or negotive, but still same-aligned and not reflected downwards through mirror as in decimal system.
 
Very often, in Estonian you write “müü” and “nüü”, in english “mu” and “nu” or “mü” and “nü” instead of the actual letter. This, because you want it at semantic, not on the acronym level where it would modify one word but not the sentence directly, where the grand conception would be reflected rather on sub-threshold level of semantical analysis.
 
Symbol of the last unknown (Õ-õõmega)
Õ-õõmega in est., where in English think how you write Õ or do you need a replacement for the character: in capital form, omega with tilde (like Ω̃), and in small form laegna-ish with small-caps version of the letter or the greek version, which looks like curved ´w. In alphabet it’s sometimes at position of ⋂, where you are not interested in infinity-long unknowns as the top unknown value, but in absolute, unreachable unknowns in regards to your current state of calculations or context, where you cannot even properly approach the actual values. For example, do stones have cognitive effects would be unreachable without capable combination of physics and biology with psychology and introspective approaches. You work with this number in regards to it’s position and possibilities, but once you get some real values after one operation you replace with ⋂, U or letter with concrete value of it, as it’s not absolutely mystical and unreachable, impossible to calculate now.
 
Symbol of Taú (the contraction of opposites)
Taú (´τ), τ with positive accent upwards (´), means connecting the opposites and could relate to Dao or Tao concept in Taoism and Daodejing.
 
What ´τ means in simple case of two opposites O and A:
  • Do the “compassionate operation” of componentiation of two ten values O and A into the same line so that R would be illuminated as being equal to T; you filter the free variables - each of four directions or two unknowns, also directions given some basic understanding of their relation to numbers, where they behave like normal digits or half-digits in different number types with lower and higher precision U; you need high-precision U to have number for each point between two neighbouring complex numbers, which is huge and each position is one digit -; so you have the positive aspect of both pointing up, the negative pointing down.
  • You solve the negative and negotive values.
  • You accept the position and resolve the posetion.
  • As a result, one “doing” (experienced negative and negotive values) is replaced with non-doing, as one non-doing (having to choose between two sets of position and posetions) is replaced with doing (you get integrated action to involve both parties of position consequences, but with the same effort).
  • In case you succeed in these operations, for example by introducing new technology or technique, or removing unneccessary complexities, you get the “win-win” property, where “win-win” aligned with “no-loss-no-loss” gives you 1´τ (latin number before a Laegna number is counting it’s whole circles, where after the number comes either the length of the circle (R) or the position (T); this is the Laegna-Latin fractional or the modulus operand “%”; in this context the Laegna number is qualitative unit, where the Latin decimals give you quantitative measures of this quality; you should consider the positional advantage of Latin numbers in indexing, where they have optimal number of digits; and advantage of Laegna numbers in aligned, frequency-based, and meaningful calculations, which are not lost in infinities, where there is less indexing and more pondering over qualities, which make the numbers cyclic and approach the rather dynamic limits and multiple dimensions in one rather “simple” number).
  • If you do it mentally, ´τ easily applies to Taoist Tao or Dao, where you can write tétaú, té taú or té´τ to connect with life vs. do´τ connecting it to computer algorithm, which is achieving mathematically equivalent behaviours and results in strictly and tautologicall qualifiable world, or ta´τ if you run these algorithms manually or operate based on your professional, scientific or well-studies background rather than personal philosophy, emotional intelligence or cognitive experience.
 
Zeta, Xeta (Exceeta) and Yeta (Yeyeeta):
Those three letters are written by corresponsing characters having beauty lines up and downwards, so that they are larger than standard letters - Z, for example has from it’s two tops two lines going slightly upwards and back from top end of the form, and going slightly downwards and front from the bottom end.
This is very poetic part and meant to be often on separate line with explanations as it does not fit normally inside the line without making it higher; it means the other end of infinity, where you start rather from extreme ⋂ and relate everything to this. Laegna infinities become complete after this one more polarity exists.
Exceeta can be used also for a letter, which looks like X, but little half-circles with two ends pointing directly outwards attached so that the center of the curve is connected to each corner of X, fitting it’s last point. This is the outside-extreme as well and it’s allowed to confuse it with xeta in varous ways as it’s complicated how the theorems differ (mainly by this X is to turn XYZ to four as needed, with outside point like ⋂, whereas the “women-system” really looks it from infinity, where the concrete logic is gone and very indirect hints might hit you.
This is special writing because normal Laegna operations are not so men-specific, but rather trivial for women (the transformation in case they express the feminine aspect). The women, they rather see the angles in infinity, social structures and things like altruist help of children and elderly, which relates to very big cycles of humanity; whereas the men see local structures such as technology, science and concrete ethics such as business (Blue Ocean strategy).
 
Various characters are more typical, which come often from transformations and other things, but they are not normalized - like you use only a few accents per sentence, you choose only a few of those letters for your whole document, because the reader must study each use case; for example special r with little black filled circle in end of the curve to express some coordinate transformations perhaps, but coordinate transforms come with theory and you cannot do several random transformations in one word just for fun without making the reading of your text extremely slow process, unrelated to normal ability to read some few paragraphs in half minutes or several pages per hour; rather, being stuck with your one word is not a good idea. In Logo design, the mathematics of Laegna numbers and letters and sounds must be reflected more deeply and creatively.
Hint: if two letters look very similar, or the accepted forms you can create, such as n and upside-down u, you must connect their meanings, which differ only by subtle nuances. While Binary systems work hard to be exact cubics, the information about infinities is lost after given number of operations and rather you work from several ends to balance your number, and cannot expect each operation to continue infinitely and logically. In several places, number system introduces some kind of “disharmonics” - you write Latin numbers and logic in metaphysical sense, looking it from a side and projecting as a square; in this sense you do Laegna logic straight-through, and all kinds of limitations of digits and numbers, as well as contradictions, errors and surrealities - rather than excluding them completely, consider that all those effects happen with real numbers in real infinities, and as you go “straight through it” with your numbers, not looking it in flat form from the side - you create a theory where in addition to you raporting the error, the actual number space is in such angle or projection, that while errors would appear when doing certain operations, they appear in number systems as well with “equivalent operations”, where by circular definition the equivalency comes from the fact that your system design is such that it develops the error into the right place. Most typical thing where to project the real errors into real places is that you work with digits, where information is lost in many cases, while with real continuous spaces and infinities, which at first place do not seem to contain digits - still, there are other effects, which appear like limitations of digits with mathematical certainty and thus design, what you mean with these errors, rather than completely avoiding them. The effect is like going straight through - the number is not a metaphysical concept, but abstract virtual reality reflecting the actual properties in the right places.
 
Compressed into to basic meanings, which might not cover all uses or aspects, but should outline the Laegna system (use sound, letter form and position in alphabet / complex numbers to understand this):
  • A - this is the material stability, repeating the natural life cycles and cycles of mathematics.
  • B - this is “on the way somewhere”, or alternatively an alternative where A is the real essential solution.
  • C - this is connecting things into such orders that they are rather in the same coordinate system than distorted in each way; such as the language (rather negatively kee or positively cee unless posetion).
  • D - this is where your series multiplies to plurar thanks to exponentiation in infinity (such as getting many children over generations), or it’s stopped and obstacled by destructive force, or it’s the natural growth of a tendency (or a “wind” in chinese martial arts) into reality in so subtle way that you won’t notice (D is like a life tunnel).
  • E - good outcome, happy end of a story, actual meaning or outcome in infinity. It could be exponent and relate to E in classical mathematics.
  • F - frequency or range of frequencies, small part of infinity, perhaps for example a meaningful vibration.
  • G - stable acceleration, opposite of D in sense of providing non-obstacled flow or gravitizing towards something.
  • H - the heavenly view, a view to something in such coordinate system where 100% H would mean it’s absolutely vertical number where normal logic is horizontal, transcending all the numbers into relation with very sharp angle upwards.
  • I - an unit, a shared introspection or philosophical world, an infinitesimal or related to imaginary unit of classical complex numbers, the i component.
  • J - connecting things like “and”, so that the result integrates both in meaningful sense.
  • K - subunit, or so small point that it’s far below zero (it’s zero squared or in laegna rather square rooted in direction of it’s zeroness).
  • L - the “left”, where you map the whole society into one number, and componentize this number to parts, getting numbers for left wing, communist, socialist or rather the unities, where behaviour of each person for example, looking this person, is measured in society in same format as you would measure direct business and ethics in right wing. R is the right wing and L is a very small number compared to R, which allows to contain the little effects you have on society as a while with your little deeds of contribution and rebellion.
  • M - a positive difference, a distance between two things, for example me and you, or two different logical units which are kind of unrelated.
  • N - lack of such difference, a positive connection between things.
  • O - unit, a closed area, such as Zero is closed to point, but has an universe inside when you zoom with Z (you could call Z a zoom, where Y is zoomout).
  • P - a stepping point, where you step into new reality; or the lack of such step, where you are below the good level of being, thus such step would appear in the future. While this is “fatal” lack of something in the past, where you see at most the Posetion of this potential, a positional version or zero-point is where you overcome this, and in Laegna system of relations of time ´P or position-P, which is used as often, relates to stepping point in now, where such lack of something existed; this could be innovation or act of creativity, overcoming fears or enlightenment or satori.
  • Q - quality.
  • R - this is the maximum reality; ´R, when moved to top octave, sees one four in sequence of A, E, I, O and another one in sequence O, P, Q, R, so if you want maximum infinity or infinity squared, which forms it’s coordinate and also the coordinate system - space of time; this kind of infinity is called R, normally used to oppose T as a Truth or Theorem to R, a coordinate system where it can be broken or reinterpreted; where the meaning appears from your shallow initial conjectures and theorems not covering the whole set of infinite possibilities; often, R is not locally infinite, but the solution moment of your theory for example.
  • S - this is locally (at O, A) going straight, but in infinity or meaning, rather fading out (if Ie=Uu) or turning back without concrete turning point in your partial math or sensory input, so you can use this rather as observation of a day than doing any generalizations. STR is important cycle as TR is imporant opposite.
  • T - theorem, ^T is Turing complex where your value implies other value to same position.
  • U - unknown.
  • V - not unknown, or a negative difference / distance / conflict between two things (in beginning of words especially) or the problem’s solution when in end of the words.
  • W - solution for V.
  • X - the visible, actual reality as you see it directly.
  • Y - a futuristic vision, a point in the future where good karmic cycle has been stabilized and as it continues to infinity, this already is infinity or part of it, not being apart from it’s straight function and oneness with itself.
  • Z - a microscopic world, a potential, or the work and process before something starts to materialize. For example, in relation to building a house and going to live in it as X, the Z of the same activity would be planning to build a house and looking ideas about where to live, which would be directed to given X and thus, where this variable was smaller than itself (remember in Laegna, opposites are not contradicting or creating alternative theories, such as war against peace and prosperity, where binary war seems to get worse, ideally, but in Laegna Logecs while you can create war theorems pointing to Negotion, the Negation itself is going upwards and in the same direction with peace, and you don’t lose the peace variables in opposite operations, where the enemy getting rich for example can not be “false” to war, as “false” to war is equally when you die - having things heads-up, where R=T and they are on the correct line, you don’t have to break all your relationship when you break a part, but naturally you go straight on and don’t wobble between “good and bad”).
 
Now, use your imagination:
  • Listen the sound, for example does “k” sound like smallest unit, starting but breaking almost at the same moment?
  • Look at the shape - doesnt K look like you point a little point, perhaps U at the center or specific value, on a short segment of some line? This should be subunit complexity in subzero space.
  • Look at the spatial logic - for example K, on real axe, is -2 and in the imaginary axe, is also -2, thus it’s a comfortable space, which is not curved and not spatially contradicting in lower frequencies (number sphere with smaller dimension where they don’t fit); rather, it clearly goes in direction of one-ness or zeroness (depending on whether you use discrete or continuous representation).
  • Look at the balanced system, where you need each character and together, they create a whole.
  • You can read those words in various directions, in various spaces and coordinate systems, getting different numbers - not one line of thought, but any complexity of ponegative frames and paradigms should give results.
  • Balance the system, for example two-letter words with some one-letter and three-letter counterparts are rather not trivially counting 1, 2 etc, but in regards to all relations they contain a balanced system of mathematecs and logecs, where any meaning is applied and considered, which you really need.
  • Words in other languages are rather accepted, providing surprising results - their laegna transformations provide meaningful associations and connotiations, as the sound and shape is really analyzed based on real human vision and senses of connections, thus it’s hard-to-avoid system and it exists based on evolution in older languages, which don’t follow exactly that - reshape the exact meanings and especially viewpoints -, but evolutionarly they fail if the sounds are too different from the meanings; I really did an intuitive operation.

Laegna Spaces

Laegna contains ten (4, 5 or 6) types of spaces - the number depends on your framework of Laegna Logic or it’s Latin implementations.
The normal space, which is approximately the width of 1 character (1 em in font design theory perhaps), is 4/4 space, whereas 1/4 width of it would be 1/4 space. 4/4 is infinity, whereas (1 to 4) / 4 is range from zero to infinity. We also utilize -1/4, compressing characters slightly closer so that they can overlap - this means negative or subzero first deccelerative space, and it’s meant as separating digits to groups not combining them, unless using special (defined?) units. 5/4 creates an acceleration, and the space is 1.25 em.
So from -0.25 to 1.25 em, there are space widths of Laegna.
Space separates words. Space-separated numbers and words are either seen as spaces replacing unknowns, U u ⋂ where with u operation (put it in the middle, in blue square and white text, or black square and white text in case you use minimal colors) means you don’t know at all what number it is, or alternatively that it’s undefined ten (like Boolean number = None in some programming languages, where “number” is the name of the variable).
In this matrix of words and space-separated numbers, in the following:
12 15 16 19.
We get such structure: we have digits, probably between 00 and 99, when we go one level up in octave to turn these complete numbers into single digits; by Second Spatial Theorem of Infinity we actually don’t need special space or range for the digits, but we use the number space zoom operations or extensions to number range, where the local number is octave-down copy of infinity (which physically, if infinity would have frequencies, would have “God’s frequencies” everywhere, and if our Soul (for our purpose, the logical unit behind the logic of our appearance as separate person, unitary termosystem [vs. some random life force on material level, which is not part of actually anything and in the fractal cannot find any units, but would just float around and do it’s work - it’s not the experience of such units in tautological theory of laegna, but the case that base mathematics creates life force mappings to mathematics based on very general description, and which forms of life exist either unitary persons or also the continuous and non-personal life force, this is now matter to research with this tautological system, which would explain the values logically, and in my case doesn’t trivially and immediately follow, especially into this base theory - I can say answer is more complex than yes or no anyway, and saying that I mean what Buddha meant in similar concepts like God or actually believing something without observation]).
💡
Okay so with Second Spatial Theorem of Infinity we are able to see the limitations of our number scope and resolve into actual, definite meaning of digits where their number space is free; to simplify we can see each value as possible frequencies, as frequency space does not overlap easily with number space - with this, we do the inverse fourier transformation kind of operation in laegna, actually simple combinatorics of letters [binary and especially my system have log and exp in whole numbers unlike decimal system, which has irrational multiplier which is even missing the nice linearities which would give it at least some sense for human psychology and not computer science]. When the digits, seen from outer octave, are separated by infinities it basically rather puts them into infinity-sized ranges, where really any number of X can somehow exist without overcoming this limit. This way, the basic effect would be that you can see this as kind of matrix.
💡
Okay if you don’t understand the Second Spatial Theorem, imagine that with spaces being like line feeds, you need to normalize each number part of space-separated system into same length, and create a matrix or Laegna “number on multiple lines”, and where it’s mathematically hard to say what now happened, you could find reasonably simple operations without complex mathematical framework. Eventually you can just read the words.
Words and sequences in numbers and words
For Laegna Numbers, in multidigit number the left digit has bigger, and the right digit has smaller value. Creating the matrix with spaces has virtual digits, which go in opposite direction - starting from smaller value and ending with bigger, so the number which would contain list of historic events would rather map the normal direction of the number, growing upwards, to same equality of number system, where you can map the two axes componentwise (each component is logical element with compass / compassion, heading each letter in it’s correct direction).
For Laegna Language, in multiletter word (which you might call multiword sentence on this acronym view, where acronym means you look at several one-digit words to turn your actual sentence into one word, where you can see the view where there are words in sentence projected from letters in a word).
First letters of the word are smaller numbers, referring to locality, past or deeper essential meaning of the origin or source of the concept. Last letters are larger numbers, referring to the general thing or the process in infinity. The sentence has first word in the biggest digit representation, and last word in the smallest.
The prefix and the suffix might be present with the fact that “1/7” or pre- and post-infinitum parts of from -0.25 to +1.25 would separate both ends of the word virtually a little over infinity, where you do not change the word but you view it in two possible interpretations or paradigms, one in which words and numbers are exactly infinity-length in their local system at least, even if the infinities could relate being of different sizes, and the other where actually 1/4 over-infinity parts are added to both ends. In reality, this reading is free and you should consider, how many letters from both ends include in the infinity, and evaluate each possible case for the word to cover possible interpretations and contexts you meant; you don’t do this in real time, but contemplate about the words and the results until you have your own simple system with some logical relations (Laegna composition is creative and perhaps you have a personal style, framework or favourite theory, where different emotions or positions apply to words - still the general result should be quite coherent). Now, as pre-infinity is inversed in non-deccelerating coordinate system, whereas post-infinity is backwards inversed or “reversed” (re meaning a cycle) in regards to the middle number; anyway, the coordinate system we use accounts them directly opposites of each other to create real opposition and not cancel it by the fact that if we reverse both, they are not in opposition, but in opposition to the word - rather the outside, bigger or future is kind of conflicting to your personal circle or contributing to it, coming from outer circle. As it’s inversed and reversed in different directions, the case of prefix and suffix themselves being opposites is mathematically stronger than the small opposition they both have to the word itself, and the future or the surrounding scope is rather unknown if you don’t include it in the calculation, in terms and not regards of this calculation.
So you have a word predetermination. I can see two prefixes - pre and de. One suffix - tion or ion. I can also measu 1/7 or 1/6 relations and relative angles of oppositions. In all cases, trivially I use my language gut or the rules of the etymological root as well, since it matters our psychology about the words and their logic is not limited to Laegna, but also to common reason and evolution of sound, where it needs to fit our symbolic instincts and necessity for common understanding and standardization. Anyway, “ion” and “tion” in reverse are “noi” and “noit”, whereas “pre” and “de” are not reversed. The word deseed would be another case, where suffix do not exist but there must be an infinity, so we can see “ed” as the suffix for consideration that it gives us at least something to analyze. We would see equal prefix and suffix.
Given this all, “pre” is the internal, local thing; whereas “tion” is the global thing it belongs into.
 
Second, we need to utilize our instincts, abilities etc.
For example while S and Z are very similar, and infinities easily reverse things, we can assume that S could be in finity what Z is in infinity, or kind of opposite in relation to x axe. Upper and lower directions are E and I, left and right are O and A, where we rotate or invert numbers. Russian “i” is like mirrored latin “n” and while incorporating Laegna ideas into Russian language, they would resonate a certain composition; while Russian would reanalyze the numbers utilizing the facts that in letters, sharp corners mean infinity angles and round corners mean local angles, less importantly lines can reach infinities while rounds are rather finite, and in regards to coordinate system, heaven is upwards and steady work is frontwards, so imagine what happens in diagonal line front and upwards - indeed, it’s approaching the balance. So now based on the diagonal law, analyze Z and it’s given meaning with function diagrams you can possibly paint, which should resolve into several, equally true, meanings!
Another example is Laegna word “impa”. “Im”, as in “impersonating”, or “immanent”, is coming from outside and penetrating you, and “pa” among other things is related to patents, where it started from lacking the position “a” and broke through with posetion-overcoming or innovative approach “p”; which meanings you can now check in dictionary - remember that “m” separates, but not from you but from universe; “m” and “n” often work where the absolute reality and wholeness is “connected”, and separate entity is “disconnected”, leaving you strong assumption that where relevant, the “unit” you first think of is yourself, the basis of your theory. Imagine that “mi” rather means me in somewhat negotive sense, than you (to achieve componentwise alignment of multidimensional laegna numbers to one dimension, often approaching one letter, opposites are often in reverse or in slight angles so that when you take all the different qualities, normalize the numbers and make sure of the compass that for example “e” value on this component would mean rather innovation or overflow than “inner space”, rather “i” - many dimensional and numerical tricks allow rather to have each component heading up and being natural parts of psychological number system, where they have funny connotiations to Latin meanings, which still allow the contextual use).
“Impa”, as a negotive word with bad energy, is impossible to spell without putting the 1/4 space into the middle - it would crack the sound frequencies or something. Only in very specific situation am I able to do this, but if you need logipedic help you should consider it’s rather special case to notice than standard language. This word, whether you write 1/4 space to show there is slight break or pause between “im” and “pa” almost unavoidably and without singing or language stretch; using our language intuition and the fact that sound frequencies, mathematical numbers, poetic meanings and more general theorems you make for your own explanations should all fit in Laegna, and factors such as however you reflect X it will remain X would remind you that if you cannot actually write the reverse, the first level of meanings contains strong U factor in it’s direction not there in Z and Y; while I have made systems to show the direction of X, such things even if they exist are not very normalized. Rather, having reflections of each number does not provide you square or a box, but unavoidable creates a complex shape and your task is sometimes to avoid that, for example not trying to use the whole system or really having notion to show what is meant, but in more normalized, standard Laegna for general readability, you consider deeply what means that “letters are mathematical functions by their shape” and “sounds are actual vibrations of those numbers” and “poetic connotations matter, for example ‘pidi’ means ‘backwards’, but using ‘pede’ for upright is really wrong for all my instincts, rather I see that two ‘e’’s as a sequence, where the growth creates linear non-growing relation, can heavily introduce unremovable posetives and you rather follow your natural instinct than creating perverse words; assuming that the word is rather what you hear“; letters or digits in numerals of complex number space are indeed normalized as computer relies less on the shape and sound, and more on the automata rules of numeric values, where the poetry comes in from the point it starts to interact with life, for example in AI system programmed on simpler math framework. We have general reasons to have both formal language and math; in this context “pede” would really just seem strange, but this is really up to the future what you decide about this strangeness - perhaps it’s not faking your business results for how numbers would remind of words; we almost inevitably have just more or less random factor where all the numbers appear, in income and outcome and other measurements, and thus the meaning of a number, you should treat it as a doctor would treat your ass, with rather professionalism - but a president candidate, with all his effort, would probably be able to normalize the coordinate axes and not write serious insults large below his image, where in infinity really bad sentences would sometimes appear just insulting the same man or calling to crime; I think switch to more dimensional number then ..but if you normalize to end result where you rather use “e”, “o”, “a” and “i”, then i would sound a little bad in contexts, but you really use it adequately then; so with general numbers it’s not a problem. If you manage to normalize your numbers extremely well, “e”-”e” linear could be improbable even in numbers; I tried many things like “tete”, but it’s rather a heavy speedup how one “pede” would measure an age (it’s the actual posetive that the girl is imagined or projected to have bigger age than she has, in Laegna either “posetive age” or “è age” or for example “ogì” which means something like times of when people did eat humans, [if this even exists as people have opinions here, but we can see some bad traits in the past following rather todays standards]).
 
Accents
Laegna words have numerous accents:
  • ˝ - e line
  • ´ - a line
  • ˙ - u line
  • ` - o line
  • `` - i line
  • ¨ - ⋂ line, the mystical reality of outside or the women word in one letter (you have to zoom or rather yoom inside).
  • ^ - situation temporarly good (arrow pointing up) or temporarly bad (instead considering the arrow outside to infinity)
  • ˇ - situation temporarly good, in local interpretation, or temporarly bad in regards to infinity
  • ~ - this is waving like S, with local conditions differing from global conditions.
  • ~~ - this is doing it twice.
  • As every rule is exact mathematical function representation, with one time meaning local, two times meaning infinity, three times meaning numbers where you already cannot count but which are not exact infinity and four times meaning infinity in power; where below there are two and above one or two accents correspondinly.
 
Important constants are R and T with ^ or ˇ accent, where they mean Turing and Riring or Rering paradoxes: one, where assigning one value to your variable actually gives it another value, so that you cannot catch that it would equal to itself; in other case, once you recognize your way it would change, so you cannot know where you are heading because you are heading only where you don’t know. Tureng or Tareng and Rereng or Rareng are solution codes for different paradoxes, as “ring” is negative or rather neutral, whereas “reng” is the position, the r-engine (english “ing” ending is accomplied by “eng”, which means engine or goaled process instead of something simply happening cycularly or continuously; engine, indeed, wants this to happen. R is the infinity and T would be in this modification an infinitesimal right next to infinity, which would be in infinities scale perhaps smaller than zero, and slowly slow down your number so that when you pass infinity, it would rather switch it’s direction or value, depending on how you exactly prepare the math and the coordinate system).
 
Accent above is either extravert or about bigger things or the social space in context of psychology and social sciences; in normalized use of Laegna it would be any accent, where negative value makes it point downwards. Where it’s U-position or the accent is alone or additionally below a letter, it’s also more or less normalized but below is the introverted value. The simples thing is to show how a person or the force you describe gives introvert values to it’s conceptions and goals, where the introvert-projected space would be equal or differ to extrovert-projected space, most typically simply meaning that you might be delusional if your personal value is upwards, but real value downwards; it could be denoted by simple posetive, but in non-normalized Laegna we get closer to many nuances, where this writing has simply more digits and dimensions to complify your algorithm.
Accent left is on O position, and right is on A position, where the number in lower octave like T numbers vs. R numbers (I and E) would also mean space or complex part as under and above mean real part. The A of previous letter might be O of the next - it’s good but if you don’t like, have small spaces of accent-size, which you can still read; if it’s not clearly visible, still the left digits are more connected to left and the right digits to the right bigger digit, where the numbers flow continuously and the U in your vision and psychology is aligned to similar U appearing in math, so you flow frontwards through the math and language, not looking it as a square of logic from the left side or up side when it’s on the floor; the latter view easily becomes to be in Latin, where numbers are not active representers as in taú ponegator (meaning a machine, where the values and opposites can shift without redefinitions, so the machine is able for Theorem of Incompleteness - to learn, for example, consciously and to set goals, also to understand concepts of having less precise results and working to make them more precise).
You can replace accents with small letters and digits above and below the letter and write even long sequences / lengths, altough it needs a reason to accept it as normalized; it’s not critical to have normalized Laegna, for example in poetry book you would easily have opposite direction to have a letter so complicated that nobody would understand, or even a letter in kind of paradox perhaps if you can find some.
In diagonals, there are the infinity numbers, you can use I, O, A, E with two upwards digits. The function of growth would mark topright corner as E, bottomleft as I, topleft as O and bottomright as A. Those directions sometimes change, but we need to consider something more “standard” and something more “specific” or “personalized”, where we don’t spend time for any kind of configurations here, or in language in any kind of surrealistic transcendendions where we could finally reach.
The exponent factor and base would be in normal positions, not in diagonals but in upper and lower parts, where the upper part has the upper line equal to the one of the letter, and the lower part has the lower line. On the other side of the base part, on left, there is the I or the case where you take root powers, where imponents are temporarly seen kind of “positions”, going directly that way and utilizing the negative or negotive components of the number; on left side from the exponent factor there is A, which correlates to that number in regards to static truth perhaps the contextual system. “Ta”, for example, would mean “him” like in Estonian but in this context it’s theorem A, an actual theorem space of proven theorems, where “Te” comes from rather chinese (Tao (道) and Te (德) are fundamental concepts in Taoism; Tao visibly connecting the opposites where the theorem would positively fall from position to negation; Taù is the automatic or logical counterpart to Tao, altough also including Tao itself as it’s operations or tautological and intuitive insights; generally it’s the Laegna Tao supporting spireason, where you don’t want to have debates with chinese - the meaning maps Tao, but it’s kind of different to do it in rational and spiritual, rather than mystical scope, so we leave Tao rather for chinese-type of intuitive understanding, and for use of exactly that word one can criticize me in being too technical and rational, too material for such a heavenly vision they could have; so we somewhat disctinct the logical machine and mystical-poetical literature into different intonations, but not exactly and completely into different conceptions).
 
You also have accents for whole words - either on right-top, little bigger than the accent of the last character in the same position would be; you would miss it easily with the character’s own right-top accent in case you are unfamiliar with the font and it’s exact sizes, but the last character of the language is the biggest, and having an accent there would have similar effect, where accent of one letter affects the whole word. Again, visual imperfection and meaningful imperfection fit. Alternatively, to be more clear, draw a curve over the word connecting it like “(” in 90-degree rotation, stretched to be above the word, and have the whole-word accent here. This accent is sometimes unusual, but it would allow to manipulate the semantic structure like you do with acronyms.
 
Opposites
 
Laegna differs in opposites:
 
Past is negative, future positive, like we would expect.
 
Usually we use destance instead of distance:
  • Destance: E is closer, I is further in terms of distance of two people; altough E is extrovert, connected world and I is introvert, disconnected world where infinity appears as prurality and negative infinity as internal metaconnection, where zero or sometimes negative infinity where we have strong opposites on other axes or another reason. I is also “me” and E is “you”, connecting that “closer” is related to you and “farther” to “me”, a separate part of the whole.
    • Use this for dimension simplification: where very different meanings of I and E fit, you can do componentwise alignation to have R=T, and then convert for example the median or the average of the resulting numbers into single number or single digit, to remove the number complexities and have the psychological effects and understanding rather than scientific talks and masterpieces of rationality. KISS is the name of engineering principle to apply here.
    • Being “apart”, for numbers, sometimes means they are in distant realms and have no connection at all; digitwise, letters “E” would mean any connections and letters “I” any lack of connections, where IIII might mean being in completely separate world - hard to achieve with normal way of distances growing where we are futher apart.
    • E is supposed to be good and I to be bad, and here we don’t like that it’s better to not make friends, which would appear.
  • “Distance” in unmodified form means I is closer and E further.
 
Usually we switch the meanings of small and big:
  • Small, in Laegna, is positive word: meaning you use less resources for the result.
  • Big is negotive, like a corporation wasting it all or the monopoly, where we can see inefficiencies.
  • On posetive axe, Smoll is small in the sense of having less of the positive resources or energy.
  • On negotive axe, Tec is the positive word of for example, utilizing a technology all over the world or having the science unions; this is correlated to techniques and technologies, which would indeed be applied everywhere and still make it smaller, for example the necessary input.
 
I play a lot with strong and weak:
  • Weak could mean delicate, a person who manages to have it all without disturbing others.
  • Strong could mean an overprotective person.
These meanings are easy to come when I see people busy with powers they don’t need, the vain attempts for sensory pleasure as Buddhist would call it - the posetive appearances.
 
Laegna contains a theorem r↔, r switch, which means each word always has a component in opposite direction. “k” is the letter which signifies that once you reach your ideal, relatively you are pressured to reach the opposite ideal - in I Ching, symbol of Heaven, we still see that yang would break when it’s exceed in strength, which is a Taoist theorem of glass and ice. Also, in laegna when you say “opposite”, you mean rather four, but in many cases you have R and T united, componentwise synchronous, into one word and then you use something visually similar to binary, and often understandable in binary terms.
 
Consonents and vocals
Numbers can mean:
  • AE is from A to E, AIE is starting from A pass I and then E. Because each component is mapped with separate infinity or in special combinatoric way, it’s still a straight line not a curve, despite appearing as curve when you are not in the system of octaves but in the one of actual values. There are complex mappings, but despite different directions of words and numbers letter- and wordwise, the time always passes from right to left, in numbers, words, sentences and space-separated numbers; unless your component analysis makes it difficult in which case you have special definitions, but you want to keep the psychological and language values rather meaningful than falling into abstract and surrealistic realm, which might exist in the real problem or number space you must have. With more complex solutions, it’s often more normalized, but indeed there are special cases and preferrations and when I speak about “normalization”, you have rather your unique style and readers, who might be for example so intelligent that they really do not stop at uttmost complexities - remember this might violate KISS unless you are young and just head to some impossible things before you get practical and minimalistic (and this is allowed, as for old success is important, but for young rather educational value matters, where compelx solutions to simple problems could even be of use, despite being the worst case - complex solutions to complex problems are sometimes required even in real world, but we have a population of humans, not geniuses, and population of genius would statistically still have supergenius; rather than growing the complexities of numbers, grow your depth of understanding). Angular numbers end with degree symbol.
  • Sometimes, AE means on higher digit (of word) it’s E and on lower, it’s A. Real numbers end with square in position and size of degree symbol.
  • Sometimes, they exist in octave space. Where with some letters, such as mapping with Z and X, you project your letters easily there, a pyramid pointing upwards would mean it’s frequential (matematecs space) or octave (logecs space) number.
 
Consonants and vocals:
  • Ti - i is on axe T, because consonants form axes, on positive side but with negotive value; finally expressing either negotive you, or negotive principle existing in Nature.
  • it - here the negotive value is on negotive position of axe T; this position for this number might be proper, so it’s rather i than ì (dot on i means it can neutrally be both, as lack of action in the world of other priorities is as close to actual counteraction as one can be, unless it’s a completely separate entity or unrelated realm).
  • ere - r, the final infinity, has e both in lows and highs; this is the vivid life, the magical journey or successful career.
  • ir - in Laegna, this means such death or disappearance that reincarnations closely do not exist, exist in the sinus vibrations, which tend to be with less and less frequency. You could use “ire” for temporary death. It rather means that i on axe of r is near-nothing. If time consists of four parts on I, O, A, E, and each part expresses an infinity or it’s power, from center point of growing (good) energy function (as for me, information energy is related to entropy, rather than opposite, as I like more memory not bigger chips, and I see energy in information); to backwards, there is the infinity of infinite times, 2013 story is what could be in the middle, and in future there is inside the same length of infinity, but outside I think the actual energy, not perhaps the physical energy in conservation laws, is creating love, integration, unity and synergy, where the effects with and without would give a relation of actual perpetuum mobile, where the rewards are either earned, philosophically or by rosetion coming from inside, not statically there, where you don’t have additional energy forms, but rather direct physical energy of things you can do like fishing and washing dishes rather than serious progress, innovation and growth and development; between those lines there is efficiency, which is comparable to having spiritual perpetuum mobile.
  • Two consonant rule: in “real”, it’s hard to say whether it’s prefix “re” with higher (e) r and high l (with l within “a” value). Alternatively, “ea” in relation to r is it’s higher value pointing downwards and in relation to l, the lower value of l is pointing downwards, but not to real lows. When they are not pointing somewhere, but connected to number sometimes the first number is more important than the second one, where each letter expects different directions and projections in it’s own context - “R” can be really strongly on position “e”, coming from “a”, which looks opposite but is supported to fact that “L” as axe is really smaller than “R”, with left being infinitesimal of global number, while right is rather the local number in it’s completeness - then, associating L with bigger and R with smaller number could also mean that we do this backwards, and this is often rather not meaningful - but rael, indeed, related to estonian and the laegna case also that “rae” is the high place where occurs the governing, especially in Estonian old language; we can see that we cannot escape the positive meaning - where “riot” would rather seek to destroy or endanger both reality and the governance, and roit also means something negotive (I don’t have my dictionary here at all now, I think I wrote this one down what I meant back then). You can analyze real languages also about patterns, which exist - as I said, magically, laegna transformations and combinations make sense, so you get existing words or very similar words with not the same, but trickily associated meanings where it’s not impossible to mean the same or to use sentences from older language, where context could matter.
 
💡
Consonants, letters on imaginary axe except where it’s “1”, represent axes or conceptions. Vocals, only the 6 letters UIOAE⋂ are rather emotional, the numeric qualities rather of good and bad associated with them. Vocals relate to nearest consonants, either arranged to directions of time or having prioritized, real value first or closer, and it’s nuances farther apart from the consonant.
 
In Laegna number systems, consonants also as imaginary components introduce space effects very easily, and with the numbers the normal space appears, where the operations see more like abstract number, but with the meaning you give it they behave well if you think consonants create the number space and vocals associate it with some actual, meaningful value of fundamental foundation or emotion not rather the “dead”, cold conception of absolute. Indeed, both have deep meaningful associations and implications / deductions, and both have real values, but it’s hard to say whether “e” is an axe or rather your success, it’s hard to imagine otherwise.
 
Laegna Complex Numbers
 
This is the table of Laegna complex numbers of scientific use, where unknowns head to ⋂, rather resolvable value in infinity of measurable scope (when you don’t have a value, you expect to solve it, not having the unknowns in your system):
ㅤ
A
O
I
E
ㅤ
ㅤ
E
E
F
G
H
ㅤ
ㅤ
A
A
B
C
D
ㅤ
ㅤ
U
U
V
W
⋂
ㅤ
ㅤ
O
O
P
Q
R
S
T
I
I
J
K
L
M
N
 
This is the table of Laegna complex numbers of philosophical use (unkowns point to omega with tilde, õ-õõmega while it might differ slightly from letter of greek), where õ-õõmega means the philosophical value you never intent to calculate so you do rather the philosopher’s thing to incorporate the unknown; the table seems very similar to scientific complex, but rather it’s having an important difference in it’s global direction and you use it for a different purpose:
ㅤ
A
O
I
E
ㅤ
ㅤ
E
E
F
G
H
ㅤ
ㅤ
A
A
B
C
D
ㅤ
ㅤ
U
U
V
W
Ω̃
ㅤ
ㅤ
O
O
P
Q
R
S
T
I
I
J
K
L
M
N
 
Real part: IOAE has the middle, the context or no-value point at A, as the T itself is on position.
Imaginary part: OPQR is having it’s neutral, non-assigned value at O, where it’s rather spatial or contextual or R value, and the space in Laegna is under the time, such as you using I and E, Z and Y - indeed, when you convert the numbers, you always expect it to be so.
 
Other letters are all consonants, thus their real number value is hardly A or 1 (neutral), but rather doing something with space and the axes.
 
With these tables, you associate the numeric position with meanings, leading you to invent new numbers and combinations - while I have some long laegna words for complex ponegations, I rather still use more or less english and estonian; while for 1, 2 and 3 digits words and some little longer, I have really good vocabulary of the simple, primitive essences, for example:
  • Tae means theorem heavily upwards, which is heaven like “Taevas” in Estonian, or the Emperors Court like “Tae” in Chinese (I don’t know whether I remembered this from past life, but I checked); since an Emperor in position relates to Heaven, especially in Chinese of given time, and the base meaning of word considers the positions - unless it’s a fake emperor, Heaven and the Highest Court are very related and the King or Emperor follows the “God” meaningfully, whatever is God or whether it even exist; if it’s Universal Truth or Love, sometimes a “definition of God”, indeed an Emperor is rather an imperir if he does not follow, or simply imbecil, which is also a heavy modification to same word - “imb”, in Laegna, definitely is far from the sky meaning that something of really low value or counteraction is approaching something meaningless rather from distance, but m is the connecting-distance so an inferior person would be simply on the way to meaningless solution; as we can interpret in several ways and maybe some are more neutral, where the obvious meaning is like that it’s not “tae”.
  • With this you got the two 3-digit words with their triviality. 2 and 3 digit words are rather trivial, and with longer words you are in the beginning really fine having 20 conceptions of Laegna Logecs, and utilizing your existing binary combinations which would be simple to utilize in Logecs given you can do a tricky thing in the middle.
 
Coordinate systems
 
Take a circle, draw a straight line around it, another with 90 degree angle to them and third with 90 degree angle to both, finally you have 8 triangles.
 
In unit sphere of Laegna, which you sometimes map to circle, you use 1 for both the radius or diameter and and circumference equal to 1. You can turn it to a square, where halves of each side can connect to themselves when broken into 180 degree angle to meet themselves, and each corner is connected to other corners, especially directly the opposite corner on straight line.
 
With 4 letters, you have 4 two-triangle pairs, which can form unit systems when you connect them, especially you can connect I with E and A with O.
 
With 4*4 system, the center 4 are on one polarity and the external four in the corners are the other polarity.
 
Sometimes you form squares, but each side is connected to real counterpart connection, and the diagonals connect to complex counterparts of connected squares in multidimensional space.
 
Sometimes, complex part is the distance from center, and the real part is the direction; where the complex part approaching infinity would create reverse ball, which closes to infinity and not locally. Properties of complex numbers allow to understand the operations and the meaning behind them.
 
These ideas are very basic - but as I have really complicated system of multiple coordinate systems, but filtering out the genius and the seed ideas, you would almost definitely reach them all with proofs of elegance over time, starting from those simple assumptions / seed ideas of excellence. Good luck combinating (not really a part of alphabet chapter, but also it’s bad if you imagine nothing or just a version of classical projection in terms of spaces and coordinates)!
 
Notice that the multidimensional spatial relations and coordinate transformations are many, and before you really understand you go many times through paradox - same time, the essence of it is quite simple and you imagine without heavy math.
 
💡
Try: tough distorted, form a square from a ball divided into 8 triangles with equal side lengths; and since there are distortions - imagine unit systems and transformations, where you get only the acceleration function from the curve (exponential space) and no contradictions or distortions; note that it’s not the normal eucleidean space or trivial extension, but rather the Laegna system.
(this is lamped block as this is really the idea, the rest is the work - indeed, you can find many new things here in the actual world where it’s not impossible to have frequencies without advanced transforms such as Fourier, which in decimals is simply insane!)
Discrete Number Systems
 
In continuous numbers, you can account that through almost any operation and relation, numbers cannot be infinities or symmetric local frequencies to infinities, directions towards - rather, for example numbers below 1, where dimensionality is not used to express the infinite attributes with units such as 1*1 would be 1 cm^2 where just 1 equals to 1 cm^1 or 1 cm -; here in discrete numbers you find out they are just that very well:
 
Using discrete numbers, the symmetries between infinities or their frequencies (where infinity properties reflect - for example musical octaves with simple-fractional harmonics such as 1/2 having two frequencies almost in the same or connected dimension, entangled, reflects in the fractal the actual property of infinity, where you would assume that while I and O differ from Í and Ó, where you have moved them above A and E vs. being just before, the case is that values below zero have the same directions to values above the first infinity line, and the closed sphere of infinity has the octaves pointing to repetition of parallel angles, thus in logical system they would be frequent - as angle just under zero is changed, it’s so close equivalent to angles just before the final 8-infinity that they would interact. The number A, at the same time, is so different from Ó, the higher infinity of the scale, that it fails to compare and the changes are not reflected in meanings of the same environment. This happens with vibrations in infinity, but the properties are reflected to finity scales of symmetric relations and multipliers - since you could actually project them info infinities.
💡
Discrete Number Infinity Alignation Theorem: the discrete numbers have numeric relations of infinities, which are lost in exponential space or the one of continuous numbers which are not fully R=T aligned unlike latin-based roots, which persist throughout the calculations. In continuous system, the property is lost for example as 0.5 * 0.5 does not give 0.75 but 0.25, but you cannot then have that a square contains more points than one of it’s edges, but it seems to have less points.
Consideration: if you use discrete numbers for easy infinities, consider that they are very well-represented with their static relations, but not convertible to continous infinities without problems, as you cannot easily separate the component values, where continous numbers tend to change the R/T relation, such as below one the relation of square is -1 (0.5 * 0.5 is square with area being half of the edge length, somewhat impossible referring to information-balanced representation of geometric shapes, where 0.5 * 0.5 should have the result containing more not less information than the base numbers; the information of point location on square needs more digits or coordinates than the information of point location on it’s edge, to represent the harmonic understanding of the values and balanced preciseness, also optimized combinatorics between zeroes and infinities, where towards infinities Laegna has huge number less combinations than Latin, where you get lost in infinity instead of averaging it by having only that number of digits available, trial and error, and some random fluctuations to probe the value space; same operations in decimal system would wobble away from infinity altogether, but if you avoid that would approach it with slower and slower pace and not very practically, as the numbers would get more and more irrational - a short words about “crazy”, something shamanic, magical or mystical, evoking the sense of mysteries in place where you could have a real number as well and do mysteries rather for deeper meaning than for automated combinations), whereas 2*2, 2 squared is 4 - here, the information balance is proper. We can see that on discrete scale, we would have proper relation of infinities, 4 being square of 2, but if we do a continuous operation such as zooming out four times, instead we have a negative reflection of infinity where bigger area instead has two inverse levels (inverse two times down) of information content, with the square having less points than the parallel or horizontal line through it, or being heavily distorted. In such way, we would lack combinatoric power - based on the balance of combinational space, which does not extend into anomaly with many possible tracks -; and we would need to have zoomed-in view of square digits to count the points according to a set of points we counted from a line; we would not have a number type, which would mean each number has reasonable, and the same class has same number of components and compatible units or the same unit.
Simplification: despite each obvious problem, we have the number space rather discrete, with finite amount of digits and combinations we can do, where infinite is rather the state of mind or a material structure than the way we express it literally; our voice vibrations can be close to infinity limits in their detail, whether we will it or don’t want. Discrete numbers usually help us through as we define that we use consistent coordinate map and do proper transformations where needed.
 
Now where in last chapter I gave you a puzzle and despite now giving some solutions I suggest to transcend the paradox of the puzzle if you can, because it actually points to something bigger - the paradox and solution of the puzzle are both welcome as the limits are important attributes of the philosophy; now I describe some discrete geometry, which differs from Eucleidean projections.
 
💡
Theorem of information treshold of pixels and bits; Theorem of Information Symmetry of (Square?) Matrices and (Pixel?) Fields: by information content, each pixel or bit is of the same size with each other, containing one single object of information; despite the pixel being square, it’s information content on diagonals is equal to it’s information content on horizontals and parallels. On screen you have the visible squareness, but in computer memory where you have the pixel matrix without it’s association to direct visual square, you don’t have this.
 
💡
Theorem of lengths in terms of pixels and bits; Theorem of Informational Distance in Discrete Fields: on square matrix or screen pixel field, to measure an information distance between two points or given pixels, you find the shortest way using diagonals, horizontals and verticals, each pixel having 8 closest neighbours (good for their Cellular Automation), and the information length is the smallest number of pixels you can use to reach from one to another.
Resulting System is not Eucleidic: as there are several shortest lines you see that the dimension is higher than Eucleid dimension and you would lose information if you use decimal complex numbers, into impossibilies of spatial structures in lower dimension.
Resulting System Represents Perfect Acceleration Function: function E in classical and Laegna mathematics is an accelerating function, and able to reach infinities based on this property; ideal function towards infinity has internal acceleration as zero. In Laegna notation, thus, numbers 1-4 as ie have their center between 2 and 3, ar in the coordinate-system-point[roint, raend]-acceleration from position 2 to position 3. Sphere mapping, by all practical purposes seems to accelerate perfectly as the resulting number systems are suitable to reach extended infinities (Laegna E (infinity-aware digit, exponent) extends infinities compared to classical E (exponent)); this discrete number system behaves similarly.
Less Irrationals: while this is projective accelerated space, not a linear space, and you would go mad of it’s initial paradoxes while able to utilize the basics - for advanced use, geometric proportions such as sinus, cosinus, pi, consist of whole numbers in such system because basically you can see which numbers and correlations you need to project the sinus function into triangle wave or square wave, the projection into curved wave is still trivial. This principle of theorem, altough in simple use of Laegna you get those properties in limited, practial amounts, means that on digits in such format, and unit sphere correlations, we use whole digits and not irrationals.
Warning against irrational numbers: they seem sane, but in actuality they are able to do secret things in places where you cannot see, and to hide their dark secrets of messing with infinity, number-karmically very bad activity. For example you don’t know infinite number of digits of Pi, but they still conspire to attack you logically, somewhere there in the hidden space, which creates a satanic illusion that it does not exist until suddenly, you see the infinite purpose as something deeply bad, because the number got bored and went to study the underworld values where still pointing to something decent and great.
 
The symmetric complex numbers:
ㅤ
A
O
I
E
E
e
f
g
h
A
a
b
c
d
O
o
p
q
r
I
i
j
k
l
 
Upfacing real numbers (you have upfacing where A is above, or frontfacing where O is above, empathizing two possible directions the diagonal can be extended with) give you this picture:
ㅤ
O
A
A
a
e
O
i
o
 
So what we need are not examples of different number systems, but basically two perfect squares - one, small, for normal numbers; another for complex numbers.
 
We need to map our discrete space of numbers into actual geometries to understand them.
 
For geometric representation of real numbers and their symmetries:
 
  • Have a square formed from four equilateral triangles.
  • You can map the square to the ball by considering it within framework of 8 projected triangles, which form the triangle divided into 8 parts of equal form and size, with three surrounding lines having 90 degree angles each with each other.
  • For first digit, you position the real number table to this square, and you get either the directed points at corners, where the points are as in number system - point value of e, for example, being the end point of it’s direction at topright corner of the main square made of four triangles. For each lower digit, you have a position or fractally repeating it inside, but to grow outwards, you add digits before ˙ such as creating aa˙ae to have bigger picture of ae; I don’t fall into nuances of positioning these, because it’s meant to be a complete and readable introduction, leaving some free space.
 
💡
Creating an Unit Ball: while two triangles form a romb, each side is of digit-length, but for it’s non-symmetric components I call the lengths U and UU for example, and solve the logical paradox of unknown with those, as they appear from unknown dimension not contained in target space.
Unit Ball has r value, where you reach a transformation on Laegna coordinate systems (once you pass madness, depression and Dark Night of the Soul appearing from paradoxes; illuminated into the number squares); in this system, projected to higher dimension, the discrete value system is reflected in spatial coordinates, where diagonals of the square are equal in projected length with it’s sides, and the free variables are available in math systems of 4.
To prove that this exists: when you extend the square system of discrete values, measured in discrete space of unit-size pixel, into infinity fractal smaller and smaller, finally you pass the point value and at that point, you have a continuous space. You can do this upwards and you have it in infinity.
 
💡
Symmetric Problems: you can get heavy problem from connecting the areas in higher space from the edges, but also from the corners, where four circles are connected with four corners. Despite this, notice that and the sphere itself you can continue your travel through those areas, with identical geometries but not losing the structure of space or getting anything illogical, even if, for example, you draw the squares on the ball. Thus, the symmetricity problem is an illusion.
 
💡
Complex fractal: you project complex number squares, in similar fractal, to what you made.
 
Number System Properties in higher-order projective space:
 
💡
Exponentiality of Sphere Geometry: such geometry, when looking innocent, will get an exponent factor to your projective system where sphere has the surface, which would get extended width outside reflecting rather acceleration coordinates, especially when projected to abstract plane.
 
💡
Calculability of Free Variables: Variable data is not lost in calculations so easily, because the irrational numbers do not hide your data into hidden corners of infinite space, providing you mere glimpses of it’s progressive bias and actual values, unless you do symbolic math.
 
💡
Rational Relations of Geometric Functions: while it’s hard to conceive the space, where you do it, you can reach understandings, where things, which behave like sinus, cosinus, pi or tangens seem relatively straightforward, such as pi is rather 4 (and with pi being four you can account of some classic math as well).
 
💡
Extensibility into octaves and higher frequencies: when you imagine that you are not on sphere, but in space where you don’t reach the same point repetitiously in the same direction, but each circle meets another point, you will have coordinate background for projecting octave data into. Numerically, you don’t need to change the coordinate system, but you add one infinity-reflecting component before the number as in: e a means a position of e’th circle or e’th repetition of the wheel; also you can use 2a to have second repetition of the circle at coordinate a, but trivially this coordinate system is not very good, being lossy - still you can make use of the concept in some important cases, where it’s more expressive.
Bridging Discrete and Continuous Systems: Exploring Numbers, Geometry, and Infinity